CERES :: Browsing by Author "Thompson, Chris"

Browsing by Author "Thompson, Chris"

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Open Access
An adaptive quasi-Newton coupled multigrid solver for the simulation of steady multiphase flows
(Cranfield University, 1997-05) Lezeau, Patrick A.; Thompson, Chris
This thesis is concerned with the application of adaptive local quasi-Newton coupled multigrid (ALQNMG) solvers to the numerical simulation of viscous incompressible fluids, using the multi-fluid model. The ALQNMG methodologyh as proven highly successful for single phase flows [1], leading to solution algorithms which are: (i) robust, (ii) efficient and (iii) accurate. Its extension to multiphase flows is very challenging because the governing equations are mathematically complex and their solutions are subject to constraints. The solver presented here has therefore required a considerable number of specific algorithmic developments. The outline of the thesis is as follows: firstly, the modelling and simulation of multiphase flows are reviewed, together with the different numerical techniques implemented in the solver. Finite volume discrete multiphase equations are then derived on structured, staggered grids. Next, having specified the solution algorithm, we consider the accuracy of the solver. Results from several test cases of varying complexity are compared with those of a widely used commercial CFD package and good agreementis obtained. The question of performance is then addressed in detail, both in terms of robustness and speed of convergence. Good accelerations are obtained using the multigrid method but the convergence rates are often not grid-independent. The most likely explanation is that the discrete operators are highly non-linear and therefore have different characteristics on different grids. Furthermore, the solution algorithm is shown to not handle certain multiphase diffusive terms very well. Convergence rates are much faster than those achieved by single grid solvers and commercial codes typically by one order of magnitude and often more, although the solver is not fully optimal. Finally, adaption is considered. Grids are generated automatically which facilitates the use of the code and allows error control. It is confirmed that multigrid methods offer a good framework for the implementation of adaption. Considerable gains in speed and memory usage, by one further order of magnitude, are achieved.
Open Access
Characteristics and forces due to slugs in an 'S' shaped riser
(Cranfield University, 2003-07) Das, I. A. F.; Thompson, Chris
The characteristics and forces due to slugs in an 'S' shaped riser have been investigated. A series of experiments were carried out using the Cranfield University Riser Test Facility, using a 9.9m high riser. Single phase (water) and two phase (air and water) tests were conducted at a system pressure of 2 bara. The two phase tests covered a range of flow regimes: severe slugging, transitional severe slugging, oscillation and normal slug flow. The two phase data was used to investigate the characteristics of severe slugging, to determine the liquid inventory in the riser downward limb and, to model the forces on a bend during the slug build-up, production and bubble penetration and gas blowdown stages of the severe slugging cycle. During the bubble penetration and gas blowdown stage, high velocities and large fluctuations in the force were observed. The resultant dynamic forces on the bend during the slug build-up and production stages were small compared to the bubble penetration and gas blowdown stage, and dominated by the hydrostatic forces due to liquid in the riser. Normal slug flow is potentially more problematic in terms of fatigue damage than severe slug flow, due to the higher velocity of the slugs coupled with large dynamic forces.
Open Access
Design, Test and Implement a Reflective Scheduler with Task Partitioning Support of a Grid
(Cranfield University, 2008-05) Ma, Yuke; Thompson, Chris
How to manage a dynamic environment and how to provide task partitioning are two key concerns when developing distributed computing applications. The emergence of Grid computing environments extends these problems. Conventional resource management systems are based on a relatively static resource model and a centralized scheduler that assigns computing resources to users. Distributed management introduces resource heterogeneity: not only the set of available resources, but even the set of resource types is constantly changing. Obviously this is unsuitable for the present Grid. In addition, the Grid provides users with the physical infrastructure to run parallel programs. Because of this increasing availability, there are more requirements for parallelization technologies. Therefore, based on problems outlined above, this thesis provides a novel scheduler which not only enables dynamic management but also provides skeleton library to support the task partition. Dynamic management is derived from the concept of reflectiveness, which allows the Grid to perform like an efficient market with some limited government controls. To supplement the reflective mechanism, this thesis integrates a statistical forecasting approach to predict the environment of the Grid in the next period. The task partitioning support is extended from the skeleton library in the parallel computing and cluster computing areas. The thesis shows how this idea can be applied in the Grid environment to simplify the user’s programming works. Later in this PhD thesis, a Petri-net based simulation methodology is introduced to examine the performance of the reflective scheduler. Moreover, a real testing environment is set up by using a reflective scheduler to run a geometry optimization application. In summary, by combining knowledge from economics, statistics, mathematics and computer science, this newly invented scheduler not only provides a convenient and efficient way to parallelize users’ tasks, but also significantly improves the performance of the Grid.
Open Access
An experimental and numerical study of flow distribution chambers
(Cranfield University, 1999-05) Wong, Voon Hon; Thompson, Chris
Flow distribution chambers are devices commonly used by the water industry to distribute flows in water and sewage treatment plants. These have simple designs, and are required to operate over a range of volumetric flowrates. Many chambers surveyed (Herbath and Wong, 1997b) were found to perform poorly. They suffered from flow mal-distribution, where the flow was not distributed according to design. The most common cause of flow mal-distribution was hypothesised to be due to the presence of a pipe bend below the chamber (Herbath and Wong, 1997a, 1997b). Therefore, an experimental and numerical study of the flow within a distribution chamber was conducted in this thesis to prove this hypothesis. A novel large-scale model (1: 13) of a typical distribution chamber was constructed. This allowed the collection of high quality and novel velocity and turbulence measurements near the free surface using hot film anemometry. The free surface location was measured using a vernier point gauge while the flow distribution between the outlets was metered by orifice plates. Records of the flow patterns were also kept. The experimental results showed that flow mal-distribution did not occur as expected since the model distribution chamber was designed with a long length of straight inlet pipe, to eliminate the suspected cause of flow mal-distribution. Novel velocity and water surface data were also collected in the experiments, which contributed towards the small body of knowledge in this area of research into flow distribution. CFD models of the physical model were created and solved using a commercial CFD code, CFX 4.1, developed by CFX International of AEA Technology. Steady state and transient two- and three-dimensional calculations of the symmetrical chamber were carried out in the course of the study. A novel adaptation of the existing code was made in obtaining solutions to the numerical models. A new solution strategy was made and refined in this stage of the research using the two-dimensional representation of the distribution chamber, for reasons of reduced computational time. Differencing schemes, surface sharpening, mass residuals, mesh refinement and different turbulence models were investigated during model refinement. The accuracies of the calculated results were determined by comparison with experimental results. It was found that the 3D model, incorporating the RNG k-c model, without surface sharpening, and using the Van Leer differencing scheme, gave good quantitative agreement with the experimental velocities, free surface location and flow distribution. The 2D results gave qualitatively good predictions. Quantitatively, the results were over-predicted which was due, to dimensional effects. The volume of the 2D model was reduced from the 3D model, while the inlet velocity was made the same. This replicated the momentum effects near the free surface that were the governing causes of flow mal-distribution. Nevertheless, this approach was much more practical in terms of computational effort. More importantly, the correct trends for flow mal-distribution could be predicted accurately. Therefore, the next stage of the research used the 2D model developed and validated here. This part of the research involved the novel adaptation of the existing symmetrical 2D results for investigating the asymmetric effects of pipe bends. Three different approaches for modelling the asymmetric effects of a pipe bend were investigated. The first, and the most simplistic, was to incline the incoming flow at an angle to the vertical. The second was to calculate the velocities and turbulence at the outlet of a simple 2D pipe bend, separate from the chamber. These calculated variables were then input into the chamber, to build up a picture of the asymmetric flow, iteratively. The third, and the most accurate method, was to couple the bend to the chamber. It was found that only the third method was capable of accurately representing the conditions within the chamber. Two different pipe bend. lengths were examined using the third approach. The distances chosen were typical of the bend distances found in some treatment plants. The results . from both simulations produced large flow mal-distribution and asymmetric flows within the chamber. A value of 10% difference between the flows from the two outlets was taken to be the maximum limit for mal-distribution. However, values of 44.5 % and 22.8 % were obtained for the larger pipe distance and short pipe distance respectively. Novel remediation strategies using numerical techniques were used to determine the most effective means of improving the flow distribution. The first, used a vertical flow splitter, placed directly above the chamber inlet. Although it altered the path of the jet, it was felt that it would be ineffective for all situations. Although the magnitude of the asymmetry was improved with the use of the splitter, the improvement was insufficient to warrant its recommendation. The other device tested was a horizontal plate located at a certain distance from the chamber inlet. For the longer bend case, a separation distance equivalent to two inlet hydraulic diameters was sufficient to deflect the jet, and reduced the magnitude of the flow asymmetry to around 2%. When the same plate location was used for the shorter bend case, the efficiency of the plate was reduced. Although there was an improvement in the distribution, the magnitude of the asymmetry was greater than 10%. The plate was subsequently lowered by half a hydraulic diameter. This gave a large improvement to the effectiveness of the plate, and the resulting asymmetry was reduced to 7.31 %. The horizontal plate was considered more promising since its function was to deflect and reduce the peak velocities of the jet. With the reduction in velocities, the magnitudes of the nonlinear terms in the Navier-Stokes equations are reduced. The solution to the equations would be more likely to be symmetrical.
Open Access
Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows
(Nanjing University of Aeronautics and Astronautics, 2015-11-24) Traczyk, Marcin; Sawko, Robert; Thompson, Chris
Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the ow. Number of closures for both breakup and coalescence can be identi ed in the literature and most of them need an estimation of model parameters that can di er even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identi cation allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup and co- alescence models over multiple cases and we propose a correlation based on non-dimensional numbers that is applicable to number of di erent ows over wide range of Reynolds numbers.
Open Access
Improvement of runback water film calculation and its impact on ice prediction
(Cranfield University, 2008-12) Soufflet, Yves; Thompson, Chris
Over the past few decades, aircraft icing has been the subject of numerous studies. Ice accretion on an aircraft can damage its aerodynamic performance. It can also have a devastating affect on structures such as high voltage pylons. The simulation of ice accretion represents an important technological breakthrough in the understanding of ice behaviour as well as an alternative to expensive experiments. Although numerical models will probably never replace wind tunnel experiments, they continuously progress and benefit from the latest advances in computing techniques. ICECREMO2 is a new generation model and uses an unstructured grid approach. Unstructured meshes offer real advantages in the generation of complex grid structures but also provide support for grid adaptivity. Adaptivity consists in improving the resolution only in some aspects of the solution. It offers the benefits of the high resolution without the computational overhead of classical structured methods. Adaptive methods are usually more difficult to implement and the application to the equation coupling water film and ice growth has never been investigated before this work. The mathematical model used in ICECREMO describes both the water film flow and the ice growth. This allows us to better predict glaze ice accretion when a runback water film is present. The equation describing the thin film water flow is a complex non-linear fourth-order degenerate partial differential equation. To resolve complex features such as a moving front, high resolution numerical methods are necessary. Such a numerical scheme has been developed for this equation in a previous study on structured grid, and has proven to be reliable. In this work Sweby's scheme has been reformulated in a finite volume framework, an error estimator has been de ned for our adaptive mesh refinement method and a grid refinement strategy has been implemented which follows the water film front and keeps it under high resolution. Finally, the impact of the improved resolution of the water film on the glaze ice growth is investigated. Results obtained with first-order and high resolution methods have been compared on different model problems under various conditions. At the end an extension of the refinement strategy is proposed by defining error estimators with respect to the ice layer and by combining it with a multi-step procedure.
Open Access
Intelligent imaging systems for automotive applications
(SPIE, 2003-03-31) Thompson, Chris; Huang, Yingping; Fu, Shan
In common with many other application areas, visual signals are becoming an increasingly important information source for many automotive applications. For several years CCD cameras have been used as research tools for a range of automotive applications. Infrared cameras, RADAR and LIDAR are other types of imaging sensors that have also been widely investigated for use in cars. This paper will describe work in this field performed in C2VIP over the last decade - starting with Night Vision Systems and looking at various other Advanced Driver Assistance Systems. Emerging from this experience, we make the following observations which are crucial for "intelligent" imaging systems: 1. Careful arrangement of sensor array. 2. Dynamic-Self-Calibration. 3. Networking and processing. 4. Fusion with other imaging sensors, both at the image level and the feature level, provides much more flexibility and reliability in complex situations. We will discuss how these problems can be addressed and what are the outstanding issues.
Open Access
Investigating gas/solid separation using a novel compact inline separator
(Cranfield University, 1999-10) White, Tyrone; Thompson, Chris
Identified as an important issue for marginal fields, the removal of sand from hydrocarbon fluids has been investigated. A review of existing sand separation equipment has recognized a need for a new separator which will satisfy the design and performance requirements necessary for protecting offshore processing equipment. This thesis details the work and analysis undertaken which has contributed towards the design and development of a new offshore gas/solid separator. A critique of different separation techniques has identified axial flow cyclone (AFC) separators as a suitable separator design for offshore desanding applications. After reviewing existing models which simulate the performance of AFC separators a simple classification table has been developed. Using the conclusions of this review as a starting platform, a methodology for developing a new computational fluid dynamics (CFD) performance model for the new separator was proposed. Experimental work undertaken at the CALtec laboratories and the BG plc (formerly British Gas Research and Technology) Low Thornley test facilities are presented. The results obtained have been used to analysis the performance of difference separator internal designs. In addition, the results have been used to evaluate the robustness of existing AFC performance models and validate the new CFD model. For the investigated operational duties, the new CFD model has been shown to consistently under-predict the collection efficiency, whereas the other AFC models over-predict. From a design point of view, a model which under-predicts the overall collection efficiency will result in the over-design of the separator for a particular operating duty. Therefore, the use of such a model will ensure the design of a separator which will offer greater than expected levels of protection of downstream equipment from erosion wear.
Open Access
Investigation on the use of raw time series and artiﬁcial neural networks for flow pattern identiﬁcation in pipelines
(Cranfield University, 2004-03) Goudinakis, George; Thompson, Chris
A new methodology was developed for ﬂow regime identiﬁcation in pipes. The method utilizes the pattern recognition abilities of Artiﬁcial Neural Networks and the unprocessed time series of a system-monitoring-signal. The methodology was tested with synthetic data from a conceptual system, liquid level indicating Capacitance signals from a Horizontal ﬂow system and with a pressure difference signal from a S-shape riser. The results showed that the signals that were generated for the conceptual system had all their patterns identiﬁed correctly with no errors what so ever. The patterns for the Horizontal ﬂow system were also classiﬁed very well with a few errors recorded due to original misclassiﬁcations of the data. The misclassiﬁcations were mainly due to subjectivity and due to signals that belonged to transition regions, hence a single label for them was not adequate. Finally the results for the S-shape riser showed also good agreement with the visual observations and the few errors that were identiﬁed were again due to original misclassiﬁcations but also to the lack of long enough time series for some ﬂow cases and the availability of less ﬂow cases for some ﬂow regimes than others. In general the methodology proved to be successful and there were a number of advantages identiﬁed for this neural network methodology in comparison to other ones and especially the feature extraction methods. These advantages were: Faster identiﬁcation of changes to the condition of the system, inexpensive suitable for a variety of pipeline geometries and more powerful on the ﬂow regime identiﬁcation, even for transitional cases.
Open Access
Mathematical and computational methods of non-Newtonian, multiphase flows
(Cranfield University, 2012) Sawko, Robert; Thompson, Chris
The research presented in this thesis is concerned with the development of numerical techniques and mathematical models for non-Newtonian uids and two-phase ows in pipes and channels. Single phase, turbulent ow calculations of non-Newtonian uids were performed initially. Based on the literature a revised approach to wall modelling is proposed and implemented. The approach uses analytical and experimental analyses of the turbulent boundary layer structure. A comparison with the standard approach is presented. The interaction between turbulence and non-Newtonian behaviour is studied by examining the rate of strain induced by uctuating components of velocity. The statistical analysis of published DNS data is performed. Finally, a model is proposed where the turbulent rate of strain is determined from turbulence quantities used by the Reynolds-averaged Navier{Stokes model and used in the calculation of molecular viscosity. For two-phase ow, the solution procedure using periodic boundary conditions was developed under an assumption of a at interface. The numerical technique was veri ed by comparing to an analytical result obtained for laminar ow in a channel. An extension to three dimensional ow is performed. With periodic boundary conditions standard turbulence models are applied to two-phase strati ed ow. Several models and their corrections for twophase ow are assessed and a new model is proposed. The numerical studies were carried out primiarily in the open-source code OpenFOAM, but initial attempts were made in commercial packages such as STAR-CD and FLUENT. Experimental data collected from the literature are used to verify the results showing good agreement in pressure drops and phase fractions.
Unknown
A new method using b-splines as shape functions and the knot insertion algorithm for shape optimization
(2007-09) Xu, Bo; Sherar, Peter A.; Thompson, Chris
A new method is developed to deal with shape optimization problems. The core idea of the method is to introduce the knot insertion algorithm which keeps the geometry unchanged while increasing the number of control points. In addition to this idea, the super-reduced idea and the mesh refinement are also employed to deal with the equality constrained optimization problem. The developed method has been tested on several applications. The first application is a Poisson equation problem. The result produced by the new method is compared with the result produced by the BFGS method because the BFGS method is considered to be one of the best methods in optimization. The result shows that the new method is more efficient than the BFGS method. The second application of the method is an airfoil design problem. The performance of using the new method is compared with the performance of using the EXTREM method in two design cases, RAE 2822 and NACA 0012. In both of these cases, the new method is much more efficient than the EXTREM method. The 3-dimensional tested case used is a mathematical problem. In this case, one finds that the discretization error is much bigger when compared with the 2-dimensional case. However the method still converges quickly to the optimum solution. As well as the above applications, the use of high order B-splines and multi-objective optimization have also been investigated. In summary, a new method is developed for shape optimization problems and validation has been carried out on several numerical examples. With the idea of the new method, it is possible to improve the efficiency of the method currently used as long as B-splines are used to describe the geometry.
Unknown
A novel approach to reduce the computation time for CFD; hybrid LES–RANS modelling on parallel computers
(Cranfield University, 2003) Turnbull, Julian; Thompson, Chris
Large Eddy Simulation is a method of obtaining high accuracy computational results for modelling fluid flow. Unfortunately it is computationally expensive limiting it to users of large parallel machines. However, it may be that the use of LES leads to an over-resolution of the problem because the bulk of the computational domain could be adequately modelled using the Reynolds averaged approach. A study has been undertaken to assess the feasibility, both in accuracy and computational efficiency of using a parallel computer to solve both LES and RANS type turbulence models on the same domain for the problem flow over a circular cylinder at Reynolds number 3 900 To do this the domain has been created and then divided into two sub-domains, one for the LES model and one for the kappa - epsilon turbulence model. The hybrid model has been developed specifically for a parallel computing environment and the user is able to allocate modelling techniques to processors in a way which enables expansion of the model to any number of processors. Computational experimentation has shown that the combination of the Smagorinsky model can be used to capture the vortex shedding from the cylinder and the information successfully passed to the kappa - epsilon model for the dissipation of the vortices further downstream. The results have been compared to high accuracy LES results and with both kappa - epsilon and Smagorinsky LES computations on the same domain. The hybrid models developed compare well with the Smagorinsky model capturing the vortex shedding with the correct periodicity. Suggestions for future work have been made to develop this idea further, and to investigate the possibility of using the technology for the modelling of mixing and fast chemical reactions based on the more accurate prediction of the turbulence levels in the LES sub-domain.
Open Access
Numerical experiments of two-phase flow in pipelines with a two-fluid compressible model
(2005-09-21T00:00:00Z) Loilier, P.; Omgba-Essama, C.; Thompson, Chris
Getting an accurate understanding of the dynamics of multiphase transport for the design of efficient pipelines is an important issue in the oil and gas industry. This paper presents simulations of one-dimensional two-phase flow in pipelines. The compressible model used is derived from the two-fluid model where pressure relaxation terms are added. The governing system consists of five time- dependent partial differential equations solved explicitly by a finite volume approach. Numerical results on well-known air-water compressible flow problems are performed and analysed. Common problems are observed with coarse meshes and are reduced with mesh refinement. We conclude that the model and the discretisation each behave well in regions of large discontinuities of pressure and velocities.
Open Access
Numerical modelling of transient gas-liquid flows (application to stratified & slug flow regimes)
(Cranfield University, 2004-04) Omgba-Essama, C.; Thompson, Chris
A new methodology was developed for the numerical simulation of transient two-phase flow in pipes. The method combines high-resolution numerical solvers and adaptive mesh refinement (AMR) techniques, and can achieve an order of magnitude improvement in computational time compared to solvers using conventional uniform grids. After a thorough analysis of the mathematical models used to describe the complex behaviour of two-phase flows, the methodology was used with three specific models in order to evaluate the robustness and accuracy of the numerical schemes developed, and to assess the ability of these models to predict two physical flow regimes, namely stratified and slug flows. The first stage of the validation work was to examine the physical correlations required for an accurate modelling of the stratified smooth and wavy flow patterns, and a new combination of existing correlations for the wall and interfacial friction factors was suggested in order to properly predict the flow features of the experimental transient case investigated. The second and final phase of the work dealt with the complex and multi-dimensional nature of slug flow. This flow regime remains a major and expensive headache for oil producers, due to its unsteady nature and high-pressure drop. The irregular flow results in poor oil/water separation, limits production and can cause flaring. The modelling approached that was adopted here is based on the two-fluid model, which can theoretically follows each formed slug and predicts its evolution, growth and decay, as it moves along the pipe. However, the slug flow study, performed here through a test case above the Inviscid Kelvin-Helmholtz transition from stratified to slug flow, showed that the incompressible two-fluid model used is unable to accurately predict most of the features of this complex flow. Mechanisms such as the interfacial wave formation, the slug growth and propagation, although observed from the simulations, cannot be accurately determined by the model.
Open Access
Numerical simulation of two-phase gas-liquid flows in inclined and vertical pipelines
(Cranfield University, 2006-08) Loilier, P.; Thompson, Chris
The present thesis describes the advances made in modelling two-phase flows in inclined pipes using a transient one-dimensional approach. The research is a developement of an existing numerical methodology, capable of simulating stratified and slugging two-phase flows in horizontal or inclined single pipes. The aim of the present work is to extend the capabilities of the approach in order (i) to account for the effect of the pipe topography in the numerical solution of the two-fluid model, and (ii) to simulate vertical bubbly twophase flows at various pressures in large diameter pipes, and (iii) to model stratified and terrain-induced slugging in two-phase flow pipelines made of several uphill, downhill and level sections. A transient compressible two-fluid model based on the one-dimensional form of the mass and momentum conservation equations for the gas and liquid phases, is developed to predict those flow configurations. The wall to fluid and the interphase interactions are accounted for by constitutive relations which are flow regime dependent. The conservation equations are discretized using a finite volume method. An algorithm is created to enable simulations on pipelines made of several sections, and account for the effect of the topography in the simulations. The methodology is applied to the compressible model in order to evaluate the robustness and accuracy of the numerical schemes, especially for the high-resolution Advection Upwinding Splitting Method (AUSM) associated to the compressible model. It also assesses the ability of the method to predict three physical flow regimes, namely stratified, bubbly and terrain-induced slug flows. The terrain-induced slugging study is performed on a slightly inclined (±1.5°) V-section system. The use of hydrodynamic slug correlations for hilly-terrain slugging is discussed. It shows to be conclusive with a good agreement with experimental measurements obtained for slug frequency and slug length predictions. Mechanisms such as the wave formation at the interface, the slug growth and propagation as well as merging slugs, can also be observed by the model. The bubbly model is extensively tested against available data collected by Nottingham University from experimental systems of 70mm and 189mm vertical pipes. In some cases, void fraction predictions are within 10% with experimental data, and pressure predictions within 4%. The simulation results compare well in overall with the measurements. In large diameter pipes, some variations are observed between the numerical and the measured results: especially the model underpredicts the flow at the bottom of the pipe. Limitations of the model for this particular case are highlighted. It is also observed that, in fully-developed flows, the model does give satisfactory predictions.
Open Access
The numerical treatment of curved boundary surfaces in an unfitted grid formulation for computational fluid dynamics
(Cranfield University, 1999-11) Gao, Zaixiang; Thompson, Chris
In this thesis a new Cartesian cut-cell scheme has been presented which solves the in- compressible Navier-Stokes equations using a finite volume approach and a staggered grid. The equations have been solved in conservation-law form upon a network of cell which were created using a Cartesian, cell-based grid generation procedure. This method used a recursive subdivision of fixed aspect ratio (Cartesian) cells creating arbitrarily shaped polygons when the Cartesian cell straddles a boundary, using a modified polygon clipping algorithm. The numerical scheme adopted is the finite volume formulation, adaptive multi- grid algorithm, and the Cartesian cut cell method. The scheme is modified to allow accurate calculation of flow variables at the intersection of curved body boundaries on non-aligned grids. A novel method to distinguish boundary cells is developed in this project. The outline of the thesis is as follows: firstly, the modelling and simulation of un- fitted Cartesian grids, structured grids, and unstructured grids are reviewed, together with the different numerical techniques implemented in the solver. Finite volume dis- crete equations are then derived on structured, staggered grid. Next, having specified the solution algorithm, we introduce the Cartesian cut cell method and consider the accuracy of the solver. Results from several test cases of varying complexity are com- pared with those of a widely used commercial CFD package and good agreement is obtained. The results of this method show that the Cartesian cut cell approach is second- order accurate for the two-dimensional flows. The question of performance of the algorithm is also addressed in detail, both in terms of robustness and speed of con- vergence by modified transformations. Good accelerations are obtained using the adaptive multigrid method but the convergence rates are often not grid-independent. Convergence rates are much faster than those achieved by single grid solvers and com- mercial codes, although the solver is not fully optimal. It is confirmed that multigrid methods offer a good framework for the implementation of grid adaptation, particu- larly in areas where the flow variable change abruptly/rapidly. Considerable gains in speed and memory usage, by one further order of magnitude, are achieved.
Open Access
Parallel unstructured solvers for linear partial differential equations
(Cranfield University, 2006-05) Becker, Dulcenéia; Thompson, Chris
This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested.
Open Access
Slug initiation and prediction using high accuracy methods - applications with field data
(Cranfield University, 2011) Kalogerakos, Stamatis; Thompson, Chris; Gourma, Mustapha
The sponsoring company of the project is BP. The framework within which the research is placed is that of the Transient Multiphase Flow Programme (TMF-4), a consortium of companies that are interested in phenomena related to ﬂow of liquids and gases, in particular with relevance to oil, water and air. The deliverables agreed for the project were: • validating EMAPS through simulations of known problems and experimental and ﬁeld data concerning slug ﬂow • introducing numerical enhancements to EMAPS • decreasing computation times in EMAPS • using multi-dimensional methods to investigate slug ﬂow The outcome of the current project has been a combination of new product development (1D multiphase code EMAPS) and a methodological innovation (use of 2D CFD for channel simulations of slugs). These are: • New computing framework composed of: – Upgraded version of 1D code EMAPS – Numerical enhancements with velocity proﬁle coeﬃcients – Validation with wave growth problem – Parallelisation of all models and sources in EMAPS – Testing suite for all sequential and parallel cases – Versioning control (SVN) and automatic testing upon code submission. • Use of 2D CFD VOF for channel simulation with: – Special initialisation techniques to allow transient simulations – Validation with wave growth problem – Mathematical perturbation analysis – Simulations of 92 experimental slug ﬂow cases The cost of uptake of the above tools is relatively small compared to the beneﬁts that are expected to follow, regarding predictions of hydrodynamic slugging. Depending on the timescales involved, it is also possible to use external consultancies in order to implement the solutions proposed, as these are software based and their uptake could be carried out in a small time-frame. Moreover it may not be necessary to build a parallel hardware infrastructure as it is now possible to have easy access to large parallel clusters and pay rates depending on use.
Open Access
Solvers on Advanced Parallel Architectures with Application to Partial Differential Equations and Discrete Optimisation
(Cranfield University, 2014-05) Czapinski, Michal; Thompson, Chris
This thesis investigates techniques for the solution of partial differential equations (PDE) on advanced parallel architectures comprising central processing units (CPU) and graphics processing units (GPU). Many physical phenomena studied by scientists and engineers are modelled with PDEs, and these are often computationally expensive to solve. This is one of the main drivers of large-scale computing development. There are many well-established PDE solvers, however they are often inherently sequential. In consequence, there is a need to redesign the existing algorithms, and to develop new methods optimised for advanced parallel architectures. This task is challenging due to the need to identify and exploit opportunities for parallelism, and to deal with communication overheads. Moreover, a wide range of parallel platforms are available — interoperability issues arise if these are employed to work together. This thesis offers several contributions. First, performance characteristics of hybrid CPU-GPU platforms are analysed in detail in three case studies. Secondly, an optimised GPU implementation of the Preconditioned Conjugate Gradients (PCG) solver is presented. Thirdly, a multi-GPU iterative solver was developed — the Distributed Block Direct Solver (DBDS). Finally, and perhaps the most significant contribution, is the innovative streaming processing for FFT-based Poisson solvers. Each of these contributions offers significant insight into the application of advanced parallel systems in scientific computing. The techniques introduced in the case studies allow us to hide most of the communication overhead on hybrid CPU-GPU platforms. The proposed PCG implementation achieves 50–68% of the theoretical GPU peak performance, and it is more than 50% faster than the state-of-the-art solution (CUSP library). DBDS follows the Block Relaxation scheme to find the solution of linear systems on hybrid CPU-GPU platforms. The convergence of DBDS has been analysed and a procedure to compute a high-quality upper bound is derived. Thanks to the novel streaming processing technique, our FFT-based Poisson solvers are the first to handle problems larger than the GPU memory, and to enable multi- GPU processing with a linear speed-up. This is a significant improvement over the existing methods, which are designed to run on a single GPU, and are limited by the device memory size. Our algorithm needs only 6.9 seconds to solve a 2D Poisson problem with 2.4 billion variables (9 GB) on two Tesla C2050 GPUs (3 GB memory).
Open Access
Time multigrid methods and D-adaptivity for coupled fluid flow solvers
(Cranfield University, 2002-02) Fernandes, Aurelio; Thompson, Chris
This Thesis is about the application of coupled multigrid solvers to the numeri- cal simulation of viscous incompressible fluids. In the centre of discussion is the adaptivity between a one-dimensional solver and a two-dimensional one. The methodology used has proved highly successful for single-and multi-phase laminar flows, leading to solution algorithms that are robust, efficient and accu- rate. The solvers presented here required a considerable number of algorithmic developments. Some of them have demanded the use of some well-known software packages. The Thesis outline is as follows: firstly, the modelling of transient single-phase and multi-phase flows is reviewed, together with a brief overview of the numerical schemes and multigrid methods used in the solvers. Secondly, the Navier-Stokes governing equations are presented and the space discretization formulas based on a control volume are formulated. After having specified the solution algorithms we present results for each solver for a set of test cases of varying complexity. Com- parison with our reference commercial code is outlined, showing good agreement in the results. Interpolation transfer operators used in the interface between the one-dimensional solver and the two-dimensional one are addressed. The coupled solvers are then applied on the numerical simulation of the transient flows on two complex multi- domain problems. Comparison results with the two-dimensional solvers have been performed. The question of performance and accuracy is addressed in detail, both in terms of robustness and speed of convergence. Good accelerations are obtained using the coupled solver. The CPU-time spent to reach the expected steady-state solution is about ten to thirty five percent of the equivalent two-dimensional solver. Considerable gains in memory usage have been achieved. The robustness has been easily verified in the comparison process with the two-dimensional transient solvers. Analytic solutions have been formulated and discussed. However some dependence on the Reynolds numbers has been observed. This was due to the geometric constraints of the complex test cases and the change of some fluid properties.